# 10.3.1 Intercepts

10.3.1 Intercepts

1. The x-intercept is the point of intersection of a straight line with the x-axis.
2. The y-intercept is the point of intersection of a straight line with the y-axis.

3. In the above diagram, the x-intercept of the straight line PQ is 6 and the y-intercept of PQ is 5.

4. If the x-intercept and y-intercept of a straight line are given,
$\overline{)\text{Gradient,}m=-\frac{y-\text{intercept}}{x-\text{intercept}}\text{}}$

Example 1:

The x-intercept of the line ST is

Solution:

The x-coordinate for the point of intersection of the straight line with x-axis is -0.4.
Therefore the x-intercept of the line ST is 0.4.

Example 2:
Find the x-intercept of the straight line 2x + 3y + 6 = 0.

Solution:
2x + 3y + 6 = 0
At x-intercept, y = 0
2x + 3(0) + 6 = 0
2x = –6
x = –3

Example 3
:
What is the y-intercept of the straight line 12x – 15y = 60?

Solution:
12x – 15y = 60
At y-intercept, x = 0
12(0) – 15y = 60
– 15y = 60
= –4